# Definition:Normal Extension/Definition 2

## Definition

Let $L / K$ be a field extension.

Let $\overline K$ be the algebraic closure of $K$.

Let $\operatorname{Gal} \left({L / K}\right)$ denote the set of embeddings of $L$ in $\overline K$ which fix $K$ pointwise.

Then $L/K$ is a normal extension if and only if:

$\sigma \left({L}\right) = L$

for each $\sigma \in \operatorname{Gal} \left({L / K}\right)$.